Slide 1
Slide 1 text
path 依存型って何?
Slide 2
Slide 2 text
.｡oO(さっちゃんですよヾ(〃l _ l)ﾉﾞ☆)
Slide 3
Slide 3 text
.｡oO(さっちゃんですよヾ(〃l _ l)ﾉﾞ☆)
好きな技術 : Erlang VM、Clojure
開發環境 : zsh、Nix、asdf、Emacs (Evil)、Vivaldi
https://ja.mackerel.io を作ってゐます
Slide 4
Slide 4 text
今讀んでゐる本
Slide 5
Slide 5 text
Scala の path 依存型って何?
調べてみました!
Slide 6
Slide 6 text
No content
Slide 7
Slide 7 text
No content
Slide 8
Slide 8 text
class A {
class B {
def f(b: B): Unit = {}
}
def newB: B = new B()
}
val a1 = new A()
val a2 = a1
val b1 = a1.newB
val b2 = a2.newB
b1.f(b1)
b1.f(b2)
?
Slide 9
Slide 9 text
class A {
class B {
def f(b: B): Unit = {}
}
def newB: B = new B()
}
val a1 = new A()
val a2 = a1
val b1 = a1.newB
val b2 = a2.newB
b1.f(b1) // OK
b1.f(b2)
// Found: Playground.a2.B
// Required: Playground.a1.B
Slide 10
Slide 10 text
No content
Slide 11
Slide 11 text
type selection x.L
↑
變數
↑
に依存
した型
type selection は名前的 (nominal)
Slide 12
Slide 12 text
type selection x.L
subtyping of types
Slide 13
Slide 13 text
type selection x.L
well-formed types
Slide 14
Slide 14 text
type selection x.L
explanation
Slide 15
Slide 15 text
trait A {
type B
def f(b: B): Unit = {}
}
trait Ba
trait Aa extends A {
type B = Ba
}
val aa = new Aa {}
aa.f(new Ba {}) // OK
val aaa: A = aa
aaa.f(new Ba {})
// Found: Object with Playground.Ba {...}
// Required: Playground.aaa.B
Slide 16
Slide 16 text
path 依存型の使ひ所
Slide 17
Slide 17 text
異なる變數から生成された値を受け附けない
class Store {
class Item {}
def getItem: Item = new Item
def save(item: Item): Unit = {}
}
val store1 = new Store
val item1 = store1.getItem
val store2 = new Store
val item2 = store2.getItem
store1.save(item1) // OK
store1.save(item2)
// Found: (Playground.item2 : Playground.store2.Item)
// Required: Playground.store1.Item
Slide 18
Slide 18 text
値を parameter として持つ型
case class Z(modulus: Int) {
sealed class Modulus {
val value = modulus
}
object Modulus {
implicit val mod: Modulus = new Modulus()
}
}
class IntMod[N <: Z#Modulus] private (val value: Long) extends AnyVal {
def +(x: IntMod[N])(implicit m: N): IntMod[N] = value + x
}
object IntMod {
import scala.language.implicitConversions
implicit def longAsIntModN[N <: Z#Modulus](i: Long)(implicit
modulus: N
): IntMod[N] =
new IntMod[N](i % modulus.value)
implicit def intModN2Long(a: IntMod[_]): Long = a.value
}
val z1 = Z(2)
val z2 = Z(10)
val i1z1 = 1: IntMod[z1.Modulus]
val i2z1 = 3: IntMod[z1.Modulus]
val i1z2 = 1: IntMod[z2.Modulus]
val i2z2 = 3: IntMod[z2.Modulus]
println(i1z1 + i2z1) // 0: IntMod[z1.Modulus]
println(i1z2 + i2z2) // 4: IntMod[z2.Modulus]
println(i1z1 + i2z2)
// Found: (Playground.i2z2 : Playground.IntMod[Playground.z2.Modulus])
// Required: Playground.IntMod[Playground.z1.Modulus]
Slide 19
Slide 19 text
實行時に確定する値に依存する型
trait time_t_proto {
type time_t
}
trait time_t_impl[U] extends time_t_proto {
type time_t = U
}
case class Ptr[U](time: U) extends time_t_impl[U]
trait Platform extends time_t_proto
object PlatformI386 extends Platform with time_t_impl[Int]
object PlatformX64 extends Platform with time_t_impl[Long]
val arch = "x86_64"
val platform: Platform =
if arch == "i386" then PlatformI386
else if arch == "x86_64" then PlatformX64
else ???
def f(timer: Ptr[platform.time_t]): platform.time_t = timer.time
val t = Ptr(42L.asInstanceOf[platform.time_t]) // C から渡される
f(t) // 42: platform.time_t
Slide 20
Slide 20 text
dependent method と
依存函數型 (dependent function type)
Slide 21
Slide 21 text
dependent method
method の引數變數に依存した型
trait V
trait A {
type B = V
def newB = new B {}
}
def f(a: A): a.B = a.newB
f(new A {}) // : V
Slide 22
Slide 22 text
依存函數型 (dependent function type)
引數變數に依存した函數型
trait A { type B; val b: B }
val f: (a: A) => a.B = (a: A) => a.b
Slide 23
Slide 23 text
dependent method や依存函數型の使ひ所
Slide 24
Slide 24 text
總稱型 (generics)
abstract class Key(name: String) { type Value }
def key[V](name: String) = new Key(name) {
override type Value = V }
class DB {
def set(k: Key, v: k.Value): Unit = {}
}
val db = new DB
val k1 = key[String]("k1")
val k2 = key[Double]("k2")
db.set(k1, "v1")
db.set(k2, 42.0)
case class Key[V](name: String) {}
class DB {
def set[V](k: Key[V], v: V): Unit = {}
}
val db = new DB
val k1 = Key[String]("k1")
val k2 = Key[Double]("k2")
db.set(k1, "v1")
db.set(k2, 42.0)
Slide 25
Slide 25 text
條件分岐
object ApplyEither {
def apply[T, F, G](t: T, f: F, g: G)(implicit ea: EApply[T, F, G]): ea.Out =
ea(t, f, g)
}
trait EApply[T, F, G] {
type Out
def apply(t: T, f: F, g: G): Out
}
object EApply {
def apply[T, F, G](implicit ea: EApply[T, F, G]) = ea
implicit def applyF[T, R, G]: EApply[T, T => R, G] =
new EApply[T, T => R, G] {
type Out = R
def apply(t: T, f: T => R, g: G) = f(t)
}
implicit def applyG[T, R, F]: EApply[T, F, T => R] =
new EApply[T, F, T => R] {
type Out = R
def apply(t: T, f: F, g: T => R) = g(t)
}
}
ApplyEither(1, { (x: Int) => 42 }, { (x: Double) => "no" }) // 42: EApply[Int, Function1[Int, Int], Function1[Double, String]].Out
ApplyEither(2.0, { (x: Int) => 42 }, { (x: Double) => "no" }) // "no": EApply[Int, Function1[Int, Int], Function1[Double, String]].Out
Slide 26
Slide 26 text
いかがでしたか?
Slide 27
Slide 27 text
參考文獻
真理について〈2〉 (ヤスパース選集 ) | カール ヤスパース, Jaspers,Karl, 靖昌, 小林 |本 | 通販 | Amazon
https://www.amazon.co.jp/dp/4650001323/
内部クラス | Scala Documentation https://docs.scala-lang.org/ja/tour/inner-classes.html
Nada Amin, Tiark Rompf, and Martin Odersky. 2014. Foundations of path-dependent types. SIGPLAN Not. 49, 10 (October 2014),
233–249. https://doi.org/10.1145/2714064.2660216
Path dependent types. Modeling algebraic structures has never… | by Marcin Rzeźnicki | VirtusLab | Medium
https://medium.com/virtuslab/path-dependent-types-9f2d7927c1fa
A quick explanation of Path Dependent Types - DEV Community
https://dev.to/markehammons/a-quick-explanation-of-path-dependent-types-4pki
Dependent Function Types | Scala 3 — Book | Scala Documentation
https://docs.scala-lang.org/scala3/book/types-dependent-function.html
Dependent Types in Scala - Some Tips, Tricks and Techniques
https://wheaties.github.io/Presentations/Scala-Dep-Types/dependent-types.html